1.) If the business was newly incorporated in November of 2015, what do I need to ask for to show proof that no more than 50 percent of its gross revenues per year are derived from one or more of the ineligible activities, such as lottery sales?
Per FinCEN's guidance (FIN-2009-G001), the higher the degree of concern you have that they may not qualify, the more due diligence you should perform to evidence their eligibility. Based on what you've described, a self-certification form signed by the customer should be sufficient. You could also review their accounts to estimate if you have no other concerns from an exemption eligibility perspective - remember that lottery revenue does not equal the volume of deposits in their lottery account.
2.) If there is currently some questionable activity involving these accounts - can we proceed with the Phase II exemption? Or would the fact that there is possible questionable activity (such as check kiting) put a stop to the exemption?
Technically, you can still exempt them (see FIN-2012-G003, question F). But that would not be prudent, in my opinion.